Generation of petawatt-class pulses with a nearly single-cycle duration or with a strongly asymmetric longitudinal profile using a thin plasma layer are investigated via particle-in-cell simulations and the analytical flying mirror model. It is shown that the transmitted pulses having a duration as short as about 4 fs (1.2 laser cycles) or one-cycle front (tail) asymmetric pulses with peak intensity of about 10^{21}W/cm^{2} can be produced by optimizing system parameters. Here, a new effect is found for the shaping of linearly polarized laser pulses, owing to which the peak amplitude of the transmitted pulse becomes larger than that of the incoming pulse, and intense harmonics are generated. Characteristics of the transmitting window are then studied for different parameters of laser pulse and plasma layer. For a circular polarization, it is shown that the flying mirror model developed for shaping laser pulses with ultrathin foils can be successfully applied to plasma layers having a thickness of about the laser wavelength, which allows the shape of the transmitted pulse to be analytically predicted.